An Inexact Inverse Power Method for Numerical Analysis of Stochastic Dynamic Systems
For researchers in numerical analysis and stochastic dynamics, this method offers a memory-efficient and convergent alternative for solving large-scale eigenvalue problems.
The paper introduces an inexact inverse power method (IIPM) for computing partial eigenvalues of large sparse matrices, demonstrating its advantages in memory usage and convergence over existing methods when applied to stochastic dynamic systems.
This paper proposes an efficient method for computing partial eigenvalues of large sparse matrices what can be called the inexact inverse power method (IIPM). It is similar to the inexact Rayleigh quotient method and inexact Jacobi-Davidson method that it uses only a low precision approximate solution for the inner iteration. But this method uses less memory than inexact Jacobi-Davidson method and has stronger convergence performance than inexact Rayleigh quotient method. We exemplify the advantages of IIPM by applying it to find the ground state in theory of stochastics. Here we need to solve hundreds of large-scale matrix. The computational results show that this approach is a particularly useful method.